Which equation correctly represents how the total mechanical energy (ME) of
a system relates to its kinetic energy (KE) and gravitational potential energy
(GPE)?

Answer:

12.5t + 8h = 259.5

t + h = 24

Step-by-step explanation:

Write one equation to deal with the costs and one equation to deal with the numbers of shirts and hats.

12.5t + 8h = 259.5

t + h = 24

Minimum percentage: 96% of the data set lies between 50 and 100.

The value of k:

Mean – (k) (sd) = lower limit

75 – 5K - 50

75 – 50 = 5k

25 = 5k

K = 5

For the percentage, we are using:

1 – 1/k^2.

1 - 1/ 25 = 24/25 = 96%

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Answer:

Θ=15

Step-by-step explanation:

AD=DC so triangle BCD is isosceles, so angle DBC = angle BCD = Θ

So angle BDC=180-Θ-Θ=180-2Θ

angle BDE = 180- angle BDC = 180-180+2Θ=2Θ

in triangle BDE all angles must add up to 180

angle BED= 180- angle BEA=180-90=90

so

90+4Θ+2Θ=180

90=6Θ

Θ=15

Answer:

Undefined

Step-by-step explanation:

The formula for slope is [ y2-y1/x2-x1 ].

0-(-3)/1-1

3/0

Since the denominator is 0, the slope is undefined.

Best of Luck!

Answer: x= -1/2 y=3/4

Step-by-step explanation:

Answer:

x = -4y + 5/2

Step-by-step explanation:

step 1: 2x +8y + -8y = 5 + -8y

2x = -8y+ 5

step 2: divide both sides by 2

2x /2 = -8y+5/2

x= -4 + 5/2

Answer:

A does, that is the only one that makes sense :)

Step-by-step explanation:

Answer:

first option

Step-by-step explanation:

if x has 2 values of y in a graph then that graph is no function

Answer:

y = 3/5x + 2

Step-by-step explanation:
Parallel lines have the same gradient, so

y = 3/5x + c

Put in your point (-5,-1):

(-1) = 3/5(-5) + c

-1 = -3 + c

-1 + 3 = c

2 = c

So

y = 3/5x + 2

The flux of the vector field F⃗ = 3(x+z)i⃗ + 2j⃗ + 3zk⃗ through the surface S is 96.

First, let's find the normal vector to the surface S. The normal vector is given by the gradient of the surface function y = x^2 + z^2. Taking the partial derivatives, we have:

∇y = ∂y/∂x i⃗ + ∂y/∂y j⃗ + ∂y/∂z k⃗

= 2x i⃗ + 0 j⃗ + 2z k⃗

= 2x i⃗ + 2z k⃗.

Now, we can compute the flux using the surface integral:

Flux = ∬S F⃗ · dS⃗,

where dS⃗ is the differential surface area vector pointing outward.

Since the surface S is defined as y = x^2 + z^2, we can rewrite it as y - x^2 - z^2 = 0.

Applying the divergence theorem, the flux can be calculated as:

Flux = ∭V (∇ · F⃗) dV,

where V is the volume enclosed by the surface S.

Let's calculate the divergence of F⃗:

∇ · F⃗ = ∂F_x/∂x + ∂F_y/∂y + ∂F_z/∂z

= 3 + 0 + 3

= 6.

Now, we can integrate the divergence over the volume V enclosed by the surface S. Since the surface is defined by 0 ≤ y ≤ 16, x ≥ 0, and z ≥ 0, we can set up the limits of integration accordingly.

Flux = ∭V (∇ · F⃗) dV

= ∫∫∫V 6 dV.

Integrating with respect to x, y, and z, we have:

Flux = ∫0∫16∫0 6 dx dy dz.

Evaluating the integral, we get:

Flux = 6 * ∫0∫16 (1) dy dz

= 6 * 16 * 1

= 96.

Therefore, the flux of the vector field F⃗ = 3(x+z)i⃗ + 2j⃗ + 3zk⃗ through the surface S is 96.

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To solve this problem, we can use the concept of combinations. We want to select 4 leaders from a group of 30 students, so the total number of ways to select 4 leaders is:

30C4 = (30*29*28*27)/(4*3*2*1) = 27,405

Now, let's consider the number of ways to select 4 leaders where no girls are selected. Since there are 16 girls in the class, we must select all 4 leaders from the group of 14 boys. The number of ways to do this is:

14C4 = (14*13*12*11)/(4*3*2*1) = 10,626

Therefore, the number of ways to select 4 leaders where at least one girl is selected is:

27,405 - 10,626 = 16,779

So there are 16,779 ways to select the 4 leaders so that at least one girl is selected.

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a) Contribution (objective value) = $132.14

b) The firm earns $132.14 at the optimal solution.

c) An additional hour of time available for the third machine is worth $0.14 to the firm.

d) An additional 5 hours of time available for the second machine will increase the objective value by $3.69.

The best result obtained from using computer software to solve the LP problem is: X1 = 11.43, X2 = 12.86, X3 = 5.71

b) The number of unused hours at the ideal solution is:

Machine 1 still has 8.57 hours of time left.

There are no hours left on Machine 2 at the moment.

There are still 94.29 hours left on Machine 3.

c) The shadow price of the third limitation is worth an extra hour of time available for the third machine. With the exception of increasing the right-hand side of the third constraint by one unit, we can solve the LP problem using the same constraints to determine the shadow price. Using LP to solve this issue, we discover that the shadow price for the third constraint is

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1.0, 3.5, 5, 6.5, 10 are the 5 number summary of the given table.

How do you find the 5 number summary?

When conducting descriptive analyses or conducting an initial analysis of a sizable data set, a five-number summary is particularly helpful. The maximum and minimum values in the data set, the lower and upper quartiles, and the median make up a summary's five values. Finding the smallest data value (minimum), the 25th percentile (Q1 - the first quartile), the median (25th percentile, Q2, the second quartile), the 75th percentile (Q3 - the third quartile), and the highest data value will yield the data set's five-number summary (maximum). The minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum make up the five-number summary. The median is the middle value; Q1 is the median of the first half of the data, and Q3 is the median of the second half.

Smallest value = 1.0

Median of the first half data Q1 = 3.5

Median Q2= 5.0

Median of the second half data Q3 = 6.5

Largest number = 10.0

The lowest is the smallest number, the maximum is the highest, the median is the intermediate value.

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Answer:

y=5/2x-5

Step-by-step explanation:

The line is interested to the graph is (2,-5)

The range of the possible values of r^2 is 0 to 1. It represents the proportion of the dependent variable’s variance that can be explained by the independent variable(s).


The coefficient of determination, often denoted as r^2, measures the proportion of the dependent variable’s variance that can be explained by the independent variable(s) in a statistical model. The value of r^2 ranges from 0 to 1.
A value of 0 for r^2 indicates that the independent variable(s) does not explain any of the variance in the dependent variable. On the other hand, a value of 1 implies that the independent variable(s) fully explain the observed variance in the dependent variable.
Therefore, the range of the possible values of r^2 is 0 to 1. Any positive numerical value within this range indicates a degree of explanatory power, while values outside this range are not meaningful in the context of r^2. It serves as a useful tool for assessing the strength of a statistical relationship and the predictive ability of a model.

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Answer:

Step-by-step explanation:

B.

The figure that represents a counterexample to the given conditional statement is option D, a Scalene Triangle.

Given that a conditional statement,

"If two angles of a triangle are congruent, then it is an isosceles triangle."

We need to determine the counterexample to this conditional statement,

A counterexample is an example that disproves a statement. In this case, if we can find a triangle where two angles are congruent but the triangle is not isosceles, it would serve as a counterexample to the given conditional statement.

A scalene triangle is a triangle where all three sides and angles are different.

If we consider a scalene triangle where two angles are congruent, it will violate the given conditional statement because it is not an isosceles triangle.

Therefore, a scalene triangle is the correct choice for a counterexample.

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Answer: y=3x-1

Step-by-step explanation:

If it’s perpendicular, the slope is the opposite reciprocal so we have:

y=3x+b

Use the point to find b

8=3(3)+b

8=9+b

Subtract 9 on both sides

B=-1

y=3x-1

Answer:

1)   Adding

2)  x = 1.5   y = 8

Step-by-step explanation:

1. Which would be a more helpful for solving the system: adding the two equations or subtracting one from the other?

Adding.

Would eliminate the y variable

2.solve the system without graphing, show your reasoning

After adding the equations

8x = 12

Divide both sides by 12

x = 1.5

Substitute into the first equation

2(1.5) + (1/2)y = 7

3 + (1/2)y = 7

(1/2)y = 4

y = 8

The required solution of the system of equations is x = 3 / 2 and y = 8.
[Adding the two equations is a more appropriate approach]

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Here,
Given a system of evaluation,

2x+1/2y=7   - - - - - - - - - (1)
6x−1/2y=5   - - -- - - -  - - -(2)

Adding equations 1 and 2
2x + 6x + 1/2y - 1/2y = 7 + 5
8x = 12
x = 12 /8
x = 3 / 2
Put x in equation 1
2 * 3 / 2 + 1/2y = 7
1/2y = 7 - 3
y = 4 * 2
y = 8

Thus, the required solution of the system of equations is x = 3 / 2 and y = 8. [Adding the two equations is a more appropriate approach].

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Answer:

Step-by-step explanation:

Let's start by assigning a variable to the number of small pizzas Tony bought. Let's call it "p".

Since Tony cut 4 of the pizzas in halves, he now has 2 pieces for each of those 4 pizzas, which means he added 4 x 2 = 8 pieces to his original amount.

The rest of the pizzas were cut into thirds. Each pizza cut into thirds gives 3 pieces. So, the number of pieces from the pizzas cut into thirds is 3(p-4).

According to the problem, the total number of pizza pieces after cutting is 18 more than the original amount. So, we can set up an equation:

3(p-4) + 8 = p + 18

Let's simplify and solve for p:

3p - 12 + 8 = p + 18

2p = 22

p = 11

Therefore, Tony bought 11 small pizzas for his birthday party.

Total number of pizzas bought by tony will be 11 .

So,

Let's start by assigning a variable to the number of small pizzas Tony bought.

Let's call it "p".

Since Tony cut 4 of the pizzas in halves, he now has 2 pieces for each of those 4 pizzas, which means he added 4 x 2 = 8 pieces to his original amount.

The rest of the pizzas were cut into thirds. Each pizza cut into thirds gives 3 pieces. So, the number of pieces from the pizzas cut into thirds is 3(p-4).

The total number of pizza pieces after cutting is 18 more than the original amount. So, we can set up an equation:

3(p-4) + 8 = p + 18

Let's simplify and solve for p:

3p - 12 + 8 = p + 18

2p = 22

p = 11

Therefore, Tony bought 11 small pizzas for his birthday party.

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The vertex, zeros, and y-intercept for the given quadratic equation f(x)=       -x² - 4x+5 are respectively,

Vertex- (2, 1)

Zeros-  (2 + i)

Y-intercept- 5

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

f(x) = y =  -x² - 4x+5

y = -x² - 4x+5

For making it perfect square, we can add and subtract square value of half of coefficient of x

So,  adding and subtracting +4 and -4 in the given equation

y = -x² - 4x+5+4-4

  = -x² - 4x+4+5-4

  = (-x +2)² +1

y-1 = (-x +2)²

So, for vertex

-x +2 = 0

x = 2

y-1 = 0

y = 1

For Zeros, y = 0

y-1 = (-x +2)²

(-x +2)² = -1

x = 2 + i,   -2-i

the zeros are imaginary

For y intercept, x = 0

y-1 = (-x +2)²

y   = 1 + (2)²

y   = 5

Hence,  vertex, zeros, and y-int. are respectively (2, 1), (2 + i), 5

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Answer:

When the two values are different

Step-by-step explanation:

Like in an inequality equation.

For example:

\(4+5x\geq 30\)

The answer would be anything greate than or equal to 30, but you would need to find x. The number line would be very useful

Hope this helps

Answer:

$1.5 per pound

Step-by-step explanation:

7.71 / 5 = 1.542

Check:

1.542 x 5 = 7.71

0.65 x 5 ≠ 7.71

Hope this helped. :)

Step-by-step explanation:

in an arithmetic sequence any new term is created by adding a defined constant to the previous term.

a1 = 2

the defined constant to be added = common difference = a2 - a1 = 11

so,

a2 = 2 + 11 = 13

a3 = a2 + 11 = a1 + 2×11 = 2 + 22 = 24

a4 = a3 + 11 = a1 + 3×11 = 2 + 33 = 35

Answer:

i dont think that you can

perhaps attatch a file of a drawing to the question you are answering for school

Step-by-step explanation:

Answer:

Answer the question according to general rules of academic writing. Use indentations; begin each paragraph with a topic sentence; support the topic sentence(s) with reasons and/or examples; use transition words to show logical organization; write a conclusion. Use correct punctuation throughout.

Step-by-step explanation:

i dont know is this what u meant lol

Answer:

-5

Step-by-step explanation:

-9+x = -14

Add 9 to each side

-9+x+9 = -14+9

x = -5

Answer:

-5

Step-by-step explanation:

You could figure out the answer by adding 9 to -14.

-14 + 9 = -5.

- When your car's speedometer reads 45 mph with the 4.65-inch tires, your tires rotate approximately 4.525 times per second.
- When you have the new 5.35-inch tires and your speedometer reads 45 mph, your car is actually traveling at approximately 3.93 rotations per second.
- When you have the new 3.75-inch tires and your speedometer reads 45 mph, your car is actually traveling at approximately 5.614 rotations per second.

Step 1: Convert the tire size to radius
To find the radius of the tire, we divide the diameter by 2. So the radius of the 4.65-inch tire is 2.325 inches.

Step 2: Find the circumference of the tire
The circumference of a circle is calculated using the formula C = 2πr, where C is the circumference and r is the radius. Plugging in the radius, we get C = 2π(2.325) = 14.579 inches.

Step 3: Calculate the number of rotations per second
To find the number of rotations per second, we need to know the linear velocity of the car. We are given that the car is traveling at 45 mph.

To convert this to inches per second, we multiply 45 mph by 5280 (the number of feet in a mile), and then divide by 60 (the number of minutes in an hour) and 60 again (the number of seconds in a minute). This gives us a linear velocity of 66 feet per second.

Next, we need to calculate the number of rotations per second. Since the circumference of the tire is 14.579 inches, for every rotation of the tire, the car moves forward by 14.579 inches. Therefore, to find the number of rotations per second, we divide the linear velocity (66 inches/second) by the circumference of the tire (14.579 inches). This gives us approximately 4.525 rotations per second.

So, when your car's speedometer reads 45 mph, the tires should rotate approximately 4.525 times per second.

Now, let's consider the scenario where you buy new 5.35-inch tires and drive with your speedometer reading 45 mph.

Step 4: Calculate the new linear velocity
Following the same steps as before, we find that the new tire has a radius of 2.675 inches (half of 5.35 inches). The circumference of the new tire is approximately 16.795 inches.

Using the linear velocity of 45 mph (66 inches/second), we divide by the new circumference of the tire (16.795 inches) to find the number of rotations per second. This gives us approximately 3.93 rotations per second.

Therefore, when you have the new 5.35-inch tires and your speedometer reads 45 mph, your car is actually traveling at approximately 3.93 rotations per second.

Lastly, let's consider the scenario where you replace your tires with 3.75-inch tires and your speedometer reads 45 mph.

Step 5: Calculate the new linear velocity
Again, using the same steps as before, we find that the new tire has a radius of 1.875 inches (half of 3.75 inches). The circumference of the new tire is approximately 11.781 inches.

Dividing the linear velocity of 45 mph (66 inches/second) by the new circumference of the tire (11.781 inches), we find that the number of rotations per second is approximately 5.614 rotations per second.

Therefore, when you have the new 3.75-inch tires and your speedometer reads 45 mph, your car is actually traveling at approximately 5.614 rotations per second.

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Answer:

Step-by-step explanation:

Set the following equations based on the question:

Solve the system by elimination, multiply the first equation by 23 and subtract the second one:

Find the value of c:

Answer:

Chaperones = 8 and Student = 117

Step-by-step explanation:

Let,

Chaperones = x

Student = y

x + y = 125

=> x = 125 - y (1)

23x + 16y = 2056

=> 23(125 - y) + 16y = 2056

=> 2875 - 23y + 16y = 2056

=> 2875 - 7y = 2056

=> 2875 - 2056 = 7y

=> 819 = 7y

=> 819/7 = y

=> 117 = y

From 1

=> x = 125 - 117

=> x = 8

To find the rate at which the diameter of the circle is changing, we'll first need to determine the relationship between the area of the circular ripple and its radius.

The area of a circle is given by the formula A = πr². In this problem, the area is increasing at a constant rate of 5 m²/second (dA/dt = 5).

Now, we'll use implicit differentiation with respect to time (t) to find the rate of change of the radius:

dA/dt = d(πr²)/dt

5 = 2πr(dr/dt)

Since we're interested in the rate of change of the diameter (D) when the radius (r) is 4 m, and D = 2r, we'll differentiate D with respect to time:

dD/dt = 2(dr/dt)

Now, we can solve for (dr/dt) when r = 4:

5 = 2π(4)(dr/dt)

5/(8π) = dr/dt

Finally, we find dD/dt:

dD/dt = 2(5/(8π))

dD/dt = 5/(4π)

So, when the radius of the circular ripple in the pond is 4 m, the diameter is changing at a rate of 5/(4π) meters per second.

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